NsThemes

This plugin insert a facebook login in your login page. 
It’s easy to install. 
You only insert your facebook code.
We test our plugins with many other. If you find incompatibility with one specific plugin, please inform us at <a href="mailto:report@nsthemes.com" rel="nofollow ugc">report@nsthemes.com</a>.

NS Social Login

This plugin add butto facebook login to your login page

mitsol

A must needed plugin to prepare your site with social medias (like facebook, twitter,etc) and search engine optimization(SEO), <a href="http://wordpress.techhelpsource.com/wp-social-integration/" rel="nofollow ugc">click here</a> to view pro version demo to understand all features.
<h4>Login by facebook(pro) :</h4>
Facebook login button along with login form are shown anywhere in page using shortcode, First time user can connect their facebook account with existing account or creating new account to login by facebook next time on one click, everything is done using ajax, there are settings to show/hide login form parts.
<h4>Basic, Open graph & twitter card(pro) meta tags:</h4>
Open Graph meta tags are required to describe your page to facebook, twitter and other social media. By WSI plugin you can easily add title, description, image, and other information which are shown anywhere in facebook when your page is liked, shared, or commented on. This ensures your branding and social presence & it is must needed to present your content efficiently across social medias like FB, twitter, google+…It also adds twitter meta tags separately(you need to enable twitter cards for your website in twitter.com to display these content).It also adds basic metadata(description, keywords..). Provides efficient, out-of-the-box search engine optimization (SEO) on a web site powered by WordPress.
It adds metadata in the following ways –
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plugin injects metadata tab at the bottom of any post edit page admin side so that you can set title, description, keywords, full meta tags, news keywords meta tags for the post(pro)
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you can set front page description and keywords from setting page which will be added in different types of front page meta tags
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Automatic addition of the blog’s tagline in the description metatag, automatic addition of the blog’s categories in the keywords metatag.
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Automatic addition of an auto-generated excerpt of the post’s or page’s content in the description meta tag. If a post has a user-defined excerpt, then this is what is used.
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Also there are different ways to set description and keywords meta tag data from different data source for other pages like Attachments, custom post types, Category-based Archives , tag-based Archives, Author-based Archives
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It injects all these metadata for all kinds of pages – single post/page, static front page, default front page, static home page, author page, attachment page etc.
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It adds required FB & twitter username/profile url input box per user so that those user relaed open graph & twitter card metadata are added when available(pro)
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It’s possible to add site-wide meta tags from setting and post edit page in admin side so that you never miss any metadata(pro)
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You can add news keywords too, some other required meta tags are added automatically(pro)
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It generates detailed metadata for the media that have been attached to the content. Considers all the media you manage in the WordPress media library(pro)
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WSI allows filtering of the generated metatags and also of some core functionality through filters. This way advanced customization of the plugin is possible. 
The available filters are:
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wp_scintg_metadata_head – applied to all metatags that have been generated by WSI. The hooked function should accept and return one argument – an array of meta tags
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wp_scintg_basic_metadata_head – applied to the basic metatags (description, keywords, etc) which were generated by WSI
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wp_scintg_opengraph_metadata_head – applied to the OpenGraph metatags that have been generated by WSI (pro)
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wp_scintg_twitter_cards_metadata_head – applied to the twitter cards metatags that have been generated by WSI (pro)
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You can see if open graph meta tags injected right or not and how it look like by submitting and checking any of your page url here – https://developers.facebook.com/tools/debug/
<h4>Social plugins(facebook):</h4>
You can add facebook social plugins like like button, follow button, send button by putting WSI social shortcodes with different parameters written in the documentation anywhere in post, page, widget, templates…pro version includes – comments, share button, embed any FB post.

WP Social Integration

WP social integration brings login by facebook, adds basic & opengraph metadata, facebook social plugins anywhere in page

NS Social Login vs WP Social Integration